Uniform estimates for transmission problems with high contrast in heat conduction and electromagnetism
Provides theoretical estimates for high-contrast transmission problems in heat conduction and electromagnetism, relevant for mathematicians and engineers modeling composite materials.
The paper proves uniform a priori estimates for transmission problems with constant coefficients on two subdomains, focusing on high contrast ratios. It handles scalar and Maxwell transmission problems, with applications to asymptotic expansions as conductivity tends to infinity.
In this paper we prove uniform a priori estimates for transmission problems with constant coefficients on two subdomains, with a special emphasis for the case when the ratio between these coefficients is large. In the most part of the work, the interface between the two subdomains is supposed to be Lipschitz. We first study a scalar transmission problem which is handled through a converging asymptotic series. Then we derive uniform a priori estimates for Maxwell transmission problem set on a domain made up of a dielectric and a highly conducting material. The technique is based on an appropriate decomposition of the electric field, whose gradient part is estimated thanks to the first part. As an application, we develop an argument for the convergence of an asymptotic expansion as the conductivity tends to infinity.